Prove that Y 1 and Y 2 are independent if and only if p ( y 1 | y 2 ) = p 1 ( y 1 ) for all values of y 1 and for all y 2 such that p 2 ( y 2 ) > 0 . Also prove that Y 1 and Y 2 are independent if and only if p ( y 2 | y 1 ) = p 2 ( y 2 ) for all values of y 2 and for all y 1 such that p 1 ( y 1 ) > 0 .

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Chapter 5.4, Problem 44E

To determine

Prove that Y1 and Y2 are independent if and only if p(y1|y2)=p1(y1) for all values of y1 and for all y2 such that p2(y2)>0.

Also prove that Y1 and Y2 are independent if and only if p(y2|y1)=p2(y2) for all values of y2 and for all y1 such that p1(y1)>0.

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Solve the following LP problem using the Extreme Point Theorem: Subject to: Maximize Z-6+4y 2+y≤8 2x + y ≤10 2,y20 Solve it using the graphical method. Guidelines for preparation for the teacher's questions: Understand the basics of Linear Programming (LP) 1. Know how to formulate an LP model. 2. Be able to identify decision variables, objective functions, and constraints. Be comfortable with graphical solutions 3. Know how to plot feasible regions and find extreme points. 4. Understand how constraints affect the solution space. Understand the Extreme Point Theorem 5. Know why solutions always occur at extreme points. 6. Be able to explain how optimization changes with different constraints. Think about real-world implications 7. Consider how removing or modifying constraints affects the solution. 8. Be prepared to explain why LP problems are used in business, economics, and operations research.

ged the variance for group 1) Different groups of male stalk-eyed flies were raised on different diets: a high nutrient corn diet vs. a low nutrient cotton wool diet. Investigators wanted to see if diet quality influenced eye-stalk length. They obtained the following data: d Diet Sample Mean Eye-stalk Length Variance in Eye-stalk d size, n (mm) Length (mm²) Corn (group 1) 21 2.05 0.0558 Cotton (group 2) 24 1.54 0.0812 =205-1.54-05T a) Construct a 95% confidence interval for the difference in mean eye-stalk length between the two diets (e.g., use group 1 - group 2).

Answer 2

Question

Chapter 5.4, Problem 44E

To determine

Prove that Y1 and Y2 are independent if and only if p(y1|y2)=p1(y1) for all values of y1 and for all y2 such that p2(y2)>0.

Also prove that Y1 and Y2 are independent if and only if p(y2|y1)=p2(y2) for all values of y2 and for all y1 such that p1(y1)>0.

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Answer 3

Question

Chapter 5.4, Problem 44E

To determine

Prove that Y1 and Y2 are independent if and only if p(y1|y2)=p1(y1) for all values of y1 and for all y2 such that p2(y2)>0.

Also prove that Y1 and Y2 are independent if and only if p(y2|y1)=p2(y2) for all values of y2 and for all y1 such that p1(y1)>0.

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Answer 4

Question

Chapter 5.4, Problem 44E

To determine

Prove that Y1 and Y2 are independent if and only if p(y1|y2)=p1(y1) for all values of y1 and for all y2 such that p2(y2)>0.

Also prove that Y1 and Y2 are independent if and only if p(y2|y1)=p2(y2) for all values of y2 and for all y1 such that p1(y1)>0.

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Answer 5

Chapter 5.4, Problem 44E

To determine

Prove that Y1 and Y2 are independent if and only if p(y1|y2)=p1(y1) for all values of y1 and for all y2 such that p2(y2)>0.

Also prove that Y1 and Y2 are independent if and only if p(y2|y1)=p2(y2) for all values of y2 and for all y1 such that p1(y1)>0.

Answer 6

Chapter 5.4, Problem 44E

To determine

Prove that Y1 and Y2 are independent if and only if p(y1|y2)=p1(y1) for all values of y1 and for all y2 such that p2(y2)>0.

Also prove that Y1 and Y2 are independent if and only if p(y2|y1)=p2(y2) for all values of y2 and for all y1 such that p1(y1)>0.

Answer 7

Chapter 5.4, Problem 44E

To determine

Prove that Y1 and Y2 are independent if and only if p(y1|y2)=p1(y1) for all values of y1 and for all y2 such that p2(y2)>0.

Also prove that Y1 and Y2 are independent if and only if p(y2|y1)=p2(y2) for all values of y2 and for all y1 such that p1(y1)>0.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 5.2 - Contracts for two construction jobs are randomly...Ch. 5.2 - Three balanced coins are tossed independently. One...Ch. 5.2 - Of nine executives in a business firm, four are...Ch. 5.2 - Given here is the joint probability function...Ch. 5.2 - Refer to Example 5.4. The joint density of Y1, the...Ch. 5.2 - Prob. 6E Ch. 5.2 - Let Y1 and Y2 have joint density function...Ch. 5.2 - Prob. 8E Ch. 5.2 - Prob. 9E Ch. 5.2 - An environmental engineer measures the amount (by...

Solution Summary: The author explains the conditional discrete probability function of Y_12, which is based on the pleft function.

Prove that Y1 and Y2 are independent if and only if p(y1|y2)=p1(y1) for all values of y1 and for all y2 such that p2(y2)>0.

Also prove that Y1 and Y2 are independent if and only if p(y2|y1)=p2(y2) for all values of y2 and for all y1 such that p1(y1)>0.

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Chapter 5 Solutions

Solution Summary: The author explains the conditional discrete probability function of Y_12, which is based on the pleft function.

Prove that Y1 and Y2 are independent if and only if p(y1|y2)=p1(y1) for all values of y1 and for all y2 such that p2(y2)>0. Also prove that Y1 and Y2 are independent if and only if p(y2|y1)=p2(y2) for all values of y2 and for all y1 such that p1(y1)>0.

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Chapter 5 Solutions

Prove that Y1 and Y2 are independent if and only if p(y1|y2)=p1(y1) for all values of y1 and for all y2 such that p2(y2)>0.

Also prove that Y1 and Y2 are independent if and only if p(y2|y1)=p2(y2) for all values of y2 and for all y1 such that p1(y1)>0.